Why does a bee have 3 eyes on its head?

The three eyes on top of the head (the ocelli) are in addition to the two compound eyes on the sides of the head.

The ocelli are simple eyes -- simple means having one lens, as opposed to compound eyes with many lenses -- but the refractive power of the lens is not sufficient to form a clear image on the photoreceptor layer so they are only suitable for light measuring functions. The lens has a large aperture and short focal length, as well as high convergence ratiOS and synaptic gains, so the ocelli are considered to be far more sensitive to light than the compound eyes. Also, the neural pathways from an ocellus to the brain are such that the ocelli are thought to respond to changes more quicly than the compound eyes.

It is commonly thought that the ocelli are used to assist in maintaining flight stability. With their underfocused nature, wide fields of view, and high light collecting ability, the ocelli are superbly adapted for measuring changes in the perceived brightness of the external world as an insect rolls or pitches around its body axis during flight. Other theories have ranged from roles as light adaptors or global excitatory organs, polarization sensors, and circadian entrainers.